This gives quite a few "pairs" (three in column two!) and only
digits 1,3,7 appear more than twice in a row, column or region.

There is probably an 'implication' chain somewhere - but where
should one be looking to locate it? I am not interested very much
in the exact location but my interest is really in WHY one should be
looking for it in that very location (where, with hindsight, it exists).

Let's take another look at this one. Using standard techniques, it can be solved to this stage:

Code:

4 29 37 5 8 27 1 69 36
1 29 8 3 24 6 7 49 5
5 6 37 9 17 147 2 48 38

7 38 9 4 13 5 6 18 2
2 38 4 6 137 17 9 5 18
6 5 1 2 9 8 3 7 4

3 14 5 7 24 9 8 126 16
8 7 6 1 5 23 4 23 9
9 14 2 8 6 34 5 13 7

Now, there is a forcing chain that involves the cells:

R5C6, R1C6, R1C2, R1C8, R1C9, R3C9, R5C9, and back to R5C6. If R5C6 = 7, the chain is in the order given. If R5C6 = 1, the chain is traced out in the reverse order. The starting cell does not matter.

Examining the "corners" of the chain, we see that:

One of R5C6 and R1C6 is 7, so R3C6 cannot contain 7.
One of R5C9 and R5C6 is 1, so R5C5 cannot contain 1.

Now, we have a BUG! Every square, except one, has only two possibilities. R7C8 can be <126>.

Take a look at the row, column, and block to which this square belongs. If the possibilities are 2 or 6, then each of these possibilities occurs twice (in the row, column or block), which is not allowed. So, R7C8 must be 1, and the rest is trivial.